In U.S. Pat. No. 5,156,151, there is disclosed a basket-like construction which is provided with a plurality of circumferentially spaced-apart arms which have outer surfaces on which a plurality of electrodes are spaced-apart longitudinally. The proximal extremity and the distal extremity of the basket-like construction are each interconnected. In the deployment of such basket-like constructions into the heart, difficulties have been encountered with the arms of the basket interfering with the mitral valve structure in the left ventricle. In addition, it has been found that the basket-like construction has a tendency to interfere with the posterior leaflet and chordae of the mitral valve and thus fails to make good contact with the posterior wall of the left ventricle. Also it has been found and there has been a tendency for the arms to become entangled in the fibrous muscle tissue in the left ventricle preventing proper deployment of the arms of the basket construction. There is therefore a need for a new and improved type of catheter construction which will overcome these difficulties.